A 100W universal motor will run just fine on a 300W True Sine Wave
inverter but not very well on a modified sine wave jobbie, and
especially not of it has a cheap (and unfiltered) speed controller, they
normally work by cutting the 50Hz sine wave into smaller or larger bits
depending on how much power you want, and if you feed one of those with
anything but sine wave currents it will most likely do just what you
describe because the limited intelligence of the speed controller
feed-backs into the rather simple inverter drive and starts resonating...

You could probably filter some of this behaviour out by adding
capacitors / reactors to the power output from the inverter but you have
to be careful in your matching of the components and you will need a
oscilloscope to do this properly...

Cheap inverters are good for restive loads but not much else...